login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A053828 Sum of digits of (n written in base 7). 19
0, 1, 2, 3, 4, 5, 6, 1, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 8, 3, 4, 5, 6, 7, 8, 9, 4, 5, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9, 10, 11, 6, 7, 8, 9, 10, 11, 12, 1, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 8, 3, 4, 5, 6, 7, 8, 9, 4, 5, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9, 10, 11, 6, 7, 8, 9, 10, 11, 12, 7, 8, 9, 10, 11 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also the fixed point of the morphism 0->{0,1,2,3,4,5,6}, 1->{1,2,3,4,5,6,7}, 2->{2,3,4,5,6,7,8}, etc. - Robert G. Wilson v, Jul 27 2006

a(n) = A138530(n,7) for n > 6. - Reinhard Zumkeller, Mar 26 2008

LINKS

Indranil Ghosh, Table of n, a(n) for n = 0..10000

Robert Walker, Self Similar Sloth Canon Number Sequences

Eric Weisstein's World of Mathematics, Digit Sum

FORMULA

From Benoit Cloitre, Dec 19 2002: (Start)

a(0)=0, a(7n+i) = a(n) + i for 0 <= i <= 6;

a(n) = n - 6*(Sum_{k>0} floor(n/7^k)) = n - 6*A054896(n). (End)

a(n) = Sum_{k>=0} A031007(n,k). - Philippe Deléham, Oct 21 2011

EXAMPLE

a(20) = 2 + 6 = 8 because 20 = 26_7.

From Omar E. Pol, Feb 21 2010: (Start)

It appears that this can be written as a triangle (see the conjecture in the entry A000120):

0,

1,2,3,4,5,6,

1,2,3,4,5,6,7,2,3,4,5,6,7,8,3,4,5,6,7,8,9,4,5,6,7,8,9,10,5,6,7,8,9,10,11,6,7,8,9,10,11,12,

1,2,3,4,5,6,7,2,3,4,5,6,7,8,3,4,5,6,7,8,9,4,5,6,7,8,9,10,5,6,7,8,9,10,11,6,7,8,9,10,11,12,7,8,9,10,11,...

where the rows converge to A173527. (End)

MATHEMATICA

Table[Plus @@ IntegerDigits[n, 7], {n, 0, 100}] (* or *)

Nest[ Flatten[ #1 /. a_Integer -> Table[a + i, {i, 0, 6}]] &, {0}, 4] (* Robert G. Wilson v, Jul 27 2006 *)

PROG

(PARI) a(n)=if(n<1, 0, if(n%7, a(n-1)+1, a(n/7)))

(PARI) a(n) = my(d=digits(n, 7)); vecsum(d); \\ Michel Marcus, Jan 07 2017

CROSSREFS

Cf. A000120, A007953, A231676-A231679.

Cf. A173527. - Omar E. Pol, Feb 21 2010

Sequence in context: A053842 A010885 A234533 * A033927 A104414 A279049

Adjacent sequences:  A053825 A053826 A053827 * A053829 A053830 A053831

KEYWORD

base,nonn

AUTHOR

Henry Bottomley, Mar 28 2000

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified June 21 23:16 EDT 2018. Contains 305646 sequences. (Running on oeis4.)